• Recent Problems

    Comparing Some Regions in a Square In the figure below, quadrilateral ABCD is a square, and E is the midpoint of the side AD . How do the areas of regions I, II, III, and IV compare?  Another way to think about this is to consider the question, What are the ratios of the areas of the

    Suppose you love chocolate. The top of each cookie is covered with the same thickness of chocolate. If you wanted to choose the cookie with more chocolate, which would you pick?
    Mara has 3 times as many dollars as her brother, Timmy. If Mara is given $20 by their mother, she will have 7 times as many dollars as Timmy. How many dollars does Timmy have?
    Grades: 6th to 8th, 9th to 12th, 3rd to 5th
    Ratio & Proportion
    Algebraic Thinking
    Analyze proportional relationships and use them to solve real-world and mathematical problems.
    Linear, Quadratic, and Exponential Models
    Building Functions
    Reasoning with Equations and Inequalities
    Creating Equations
    Use functions to model relationships between quantities.
    Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
    Represent and analyze quantitative relationships between dependent and independent variables.
    Reason about and solve one-variable equations and inequalities.
    Multiply and divide within 100.
    3.OA.C.7, 6.EE.B.6, 6.EE.C.9, 7.EE.B.4a, 8.F.B.4, HSA-CED.A.2, HSA-CED.A.3, HSA-REI.A.1, HSF-BF.A.1a, HSF-LE.A.2, 7.RP.A.2c
    If each side of the triangle in Figure 1 is 1 inch long, this means the triangle has a perimeter of 3 inches. Suppose you continued the pattern in the diagram until you reached Figure 5. What is the sum of the perimeters of all the white triangles in Figure 5?
    Grades: 9th to 12th, 3rd to 5th
    Algebraic Thinking
    Measurement & Data
    Interpreting Functions
    Generate and analyze patterns.
    Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
    Solve problems involving the four operations, and identify and explain patterns in arithmetic.
    3.OA.D.9, 3.MD.D.8, 4.OA.C.5, HSF-IF.A.3

    In the Sudoku grid at left, only the numbers along the perimeter are shown.

    Suppose the grid was completed according to the standard Sudoku rules — each row, column and 3 × 3 square contains the numbers 1–9. Would the sum of all the missing numbers be divisible by 3?

  • Connect with NCTM Illuminations

    Facebook icon Twitter icon YouTube icon Google+ icon Pinterest icon